A conditional compound Poisson process approach to the sparse Erd\H{o}s-R\'enyi random graphs: moderate deviations
| Autor: | Sun, Wen |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We construct a compound Poisson process conditioned on its random summation that represents the sizes of the connected components in the sparse Erd\H{o}s-R\'enyi random graph $G(n,c/n)$. This new representation depicts a connection between the phase transition in the sparse random graph and the condensation transition in the zero-range model. Under this framework, we can derive moderate deviation principles for the maximun component, total number of connected components and empirical measure of the sizes in the non-critical regimes. Large deviation results are discussed. Comment: 34 pages |
| Databáze: | arXiv |
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